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Issue 6 (2014) - Numbers

Editorial — Numbers in Early Modern Writing

Katherine Hunt and Rebecca Tomlin

[1] ‘Here’s another of your ciphers to fill up the number’. John Ford’s choice of insult, a derogatory description of a gallant, spoken by the nurse Puttana in ’Tis Pity She’s a Whore (c.1629; I.ii.110-111) is revealing in a number of ways. The ‘cipher’ here is a nothing, a man of little worth, making up the numbers of a young lady’s gaggle of suitors, but he seems nevertheless to have some substance, because he ‘fill[s] up the number’. In this throwaway line is contained the derogatory dismissal of this useless gallant; the partial reversal of the gendered implications of the cipher (the empty zero more usually being associated with woman, and the phallic 1 with man); and also a hint at a relatively new understanding, in popular mathematics, of just what a cipher might be able to do. The cipher, or zero, in Hindu-Arabic notation, is worthless alone but, placed after another number in written notation, it fills up the number by multiplying it by a factor of ten. This function of the cipher is not a new idea; nor is Ford’s a novel application of it to literature. But the number joke is telling nonetheless, indicating the increasing familiarity, in this period, with Hindu-Arabic notation and the new mathematics, in which numbers were calculated in writing rather than using counting aids; indeed, the word ‘ciphering’ began in this period to be applied not just to writing zeroes but to numbers more generally. Not only does Ford expect the audience to understand an arithmetical joke about the place value of the cipher, but he gives the joke to a low-status, female, domestic servant. In fact, in Ford’s play the well-bred lady, Annabella, does not respond to Puttana’s comment or engage in the numerical chatter and Puttana, as her name indicates, turns out to be a thoroughly unwise advisor to her young mistress. But Puttana’s jibe nevertheless allows us to trace the outlines of ambivalent early modern attitudes to number: it is at once a fluid and vivid source of metaphors and jokes, especially ones which rely on a sophisticated level of knowledge about the written language of number in order to be understood; but it is also the material of whores and servants, tradesmen and the lower classes.

[2] This special issue of the Journal of the Northern Renaissance investigates how contemporary developments in written, and particularly printed, works on and of numbers both reflected and shaped the creative works of the period and how such novel concepts as the cipher, unity and equivalence, fractions, and the spatial aspects of written number were given significance beyond arithmetic in poetry, on stage, and in prose. The numbers that fill early modern books oscillate between practicality and mystery, materiality and abstraction, application and theory. What were the practical issues arising from printing numerical texts, and how were numbers represented on the page? How were early modern literary writers influenced by developments in theoretical and applied arithmetic and, conversely, is it possible to trace the influence of what seemed to be purely literary forms on the development of numerical writing? Such questions were the basis of ‘Working it out: numbers in early modern writing’, a multidisciplinary conference we organised at Birkbeck in 2013, and from which this collection of essays has developed. Some of the papers included here were first given at the conference; all show the rich and diverse readings of early modern numerical culture developing in recent work from both sides of the Atlantic.

[3] A thread running through many papers at the conference, and the chronological and intellectual starting point for this issue, is the work of Robert Recorde. His The Ground of Artes, probably first published in 1543, was the first arithmetical textbook to be written originally in English (translated books had appeared earlier in the century); it introduced Hindu-Arabic notation and the new mathematics to the English vernacular. The book proved popular and influential and was issued in forty-five editions, with various additions but relatively few subtractions, until 1699. Over the century and a half that divides the first and the last editions of the Ground, the English writing of numbers changed. With the help of Recorde’s self-consciously didactic textbook, English people, among others, took up en masse what he called ‘Arithmetyke with the penne’ (Recorde 1543: sig.116v). Hindu-Arabic notation took over from Roman as the principal figures used for calculation and Roman letters-as-numbers slowly lost their practical value, leading to new relationships between letters and numbers. Writing about numerical calculation reflexively concerned itself with calculations done in writing, not manually with counters or an abacus; although Recorde did include a section on calculating with counters it was tucked away at the end of the first volume of his book, always somewhat marginal to his main project, intended either for ‘them that can not write and rede’ or for those who ‘have not a some tymes theyr penne or tables redye with them’ (Recorde 1543: sig.116v). This section persisted in later editions of the book, until the final edition in 1699 when the instructions for reckoning by counters were at last left out. ‘Arithmetyke with the penne’, or ciphering, had definitively won; although people surely continued to use counters or fingers to reckon with, numbers were now things primarily to be written and read, and manipulated on the page. Calculation was no longer an ephemeral activity, lost as soon as the counters that embodied it were moved, but was now a process of writing and, by writing, recording. The publication history of The Ground of Artes provides, then, both a start and an end point for this special issue: it bookends the period in which, in England, numbers moved from the counter table to the page, from the material object to the written symbol.

[4] Any understanding of numbers in the period must grapple with the spread of their use: who used numbers and to what purpose. Given that this was a period in which numbers turned into things that were principally written, it is tempting to draw up a standard by which to measure numeracy analogous to that used to determine literacy (although the latter term is also problematic). In fact, as Keith Thomas argues in an important article, it is much harder to assess popular numeracy than literacy (Thomas 1987). Numeracy is, in one sense, innate: one doesn’t need to be able to read and write to tell that two apples are more than one, for instance. But such examples are in fact very limited: the number sense is culturally and historically determined, and has to be learned; the innate knowledge that two is more than one only goes so far. And in any case degrees of early modern numeracy were very varied, and many people would know only the number work that was immediately relevant to their professional needs; as Thomas suggests, while many early modern people would have had a basic ability to add and subtract, knowledge of multiplication and division was, to modern sensibilities, surprisingly restricted. Arithmetic was not part of the usual grammar school curriculum (Thomas 1987: 109-110) and, though it was part of the quadrivium, much of what we would now class as basic mathematics went unlearned by students at the universities. This is not to suggest that the tradesman was somehow more progressive than the scholar: Mordechai Feingold (1984) has conclusively shown the complex links between the two, and the sophistication of the work being done in the universities. A recurring theme of the articles in this special edition is the tension over number work and the extent to which it was the preserve of an intellectual elite, or utilised by the trades and the applied arts. Much of the number work discussed here is related less to the mathematical discoveries of the universities and more to tradesmen’s shop arithmetic: but also to the relationship, in this period, of the latter to the former. Our authors show how the middle ground between the two was appropriated by the literary imagination and the material book culture of the early modern period.

[5] Practical, applied mathematics put numbers to work in the world. As knowledge of the new mathematics was disseminated — as printed numbers became much more commonplace, and reckoning by pen overtook mercantile computation with abacus or counting board — the material qualities of these numbers-in-the-world took on new or augmented forms. Understanding of the features of written numbers and the ways in which they might be manipulated permeated the wider culture, arithmetic books with their pages of printed numbers could be found in many more homes, and mathematical concepts became available to an ever-widening range of people. Recent work by John Denniss (2009), Kathryn James (2011), Benjamin Wardhaugh (2012, 2014), and Travis Williams (2012, 2013), has explored the pedagogical, the literary, and the material characteristics of books in which mathematics was taught and learned, from Recorde onwards. As Kathryn James suggests, over the course of the sixteenth century ‘an informal vernacular popular literature of mathematics emerged’ in England (James 2011: 4); articles collected in the present issue investigate different aspects of the implications of this increasing familiarity with written numbers for literary and material culture, as written numbers became more common in both manuscript and print.

[6] Given that the popular understanding of written numbers changed over this period, how did this affect numbers in writing, both literary and less so? Looking as we are from the twenty-first century, from a world described by binary code and big data and with an emphasis on metrics, accounting, quantifying and digitising, is it possible to comprehend the strangeness and novelty of the new mathematics introduced to England in the sixteenth century? In recent years, as part of the turn in literary studies towards the history of science and perhaps inspired by our contemporary drive to quantify and to measure, scholars have become interested in the intersection of mathematics and early modern literature. Whereas twentieth-century numerological readings of Renaissance texts discussed the mystical potential of numbers, this new work investigates how practical, applied mathematics interacted with literary production. Recent studies have examined the intersection of literature with calculation and quantification (Glimp and Warren 2004); measurement and mis-measurement (Blank 2006); the zero or cipher (Ostashevsky 2004, Parker 2009); geometry and spatial reasoning (Mazzio 2004, Turner 2006); developments in algebra and arithmetic, counting and accounting, including double-entry bookkeeping (Poovey 1998, Raman 2008 and 2010, Smyth 2010, Wilson-Lee 2013, Woodbridge 2010); and financial trends more generally, in studies which move on from New Economic Criticism (see for example Korda 2002, 2009, and 2011; Sullivan 2002).

[7] What these works share, with each other and with the present collection, is a conviction that modes of numerical thought — and the ways of thinking and doing that characterized practical mathematics — influenced the literature of the early modern period. These studies insist that number work was productive for literature; the essays collected here argue too that literature, and other cultural forms, was productive for number work. From the poetry of Shakespeare and Donne, to accounting and fencing and cryptography, the essays we present here traverse the boundaries between literary and numerical writing. The papers share an epistemological concern with what is known about number and how that is reflected in the various cultural products that are their subject matter. Together, they show us that forms of literary production— conceptual and material — affected the writing of number, as well as the other way round.

[8] The shift to ciphering brought to the workings of numbers both clarity and new kinds of complication. Ephemeral numbering by gesturing hands and moving counters was pinned to the page by the new mathematics, but this was not a straightforward shift from messy body to tidy book. Puttana suggests as much in her description of the empty-headed gallant as a ‘cipher’, his value as a man limited to his ability to ‘fill up the number’, connecting the place value of numbers to their spatial and embodied dimension in the early modern imagination. The numbers on the page, a material manifestation of the abstract, were a way to comprehend the material world, but also, paradoxically, to articulate its bewildering intangibles. The material world is not always tractable and these essays, countering the anticipated orderliness of number work, explore the tensions that sometimes arise between the things that are countable and abstract numeration.

[9] Our opening article, by Lisa Wilde, examines just such complexity in the text that forms the starting-point of this issue, Robert Recorde’s The Ground of Artes (1543). Wilde employs a close reading of this book to investigate and to question some ideas about popular numeracy in the middle of the sixteenth century, and evaluates the importance of this book in the effort to shape algorism into a body of knowledge accessible to the early modern reader. The pedagogical tactics of the Ground, Wilde argues, situate it within the late-medieval scholastic tradition which places emphasis on reason as the basis of understanding. However, the text also sometimes puts reason to one side in favour of ‘practical logic’ — here is arithmetic as practical craft, related to techne rather than episteme; something corporeal, and at times openly illogical. In uncovering some of the ‘messy realities of […] popular numeracy’, Wilde allows Recorde’s text to emerge as one which is often problematic, showing up the tensions and potential antagonisms involved in the early modern adoption and practical application of Hindu-Arabic notation.

[10] Ken Mondschein’s article, on Camillo Agrippa’s Treatise on Arms (1553), takes us beyond English writing to explore the relationship between arithmetic in the abstract and its application to the physical world. This innovative fencing manual adopts, Mondschein argues, the principles of Euclidean geometry (number in space), and Aristotelian concepts of time (number in time), and applies them to the human body in action. He shows how Agrippa reflected and contributed to the vernacularisation of the mathematical conception of the world and the idea of number as the underpinning of reality. Agrippa’s application of a set of core geometrical and numerical principles to a complicated physical practice is based on experience, not theory, and acts as something of a bridge between an allegorical deployment of numbers and a scientific one. The article offers a brief overview of numerical conceptions in Italian fencing books as a context for Agrippa’s contributions and legacy and argues that these, together with the works of Agrippa’s successor Girard Thibault, were enumerations of the universe and the human operatives within it which reflected and disseminated the ‘Scientific Revolution’.

[11] In her article, Rebecca Tomlin considers the self-fashioning of early modern authors of works on numbers. She offers a material-text-based reading of James Peele’s two books on double entry book-keeping, The maner and fourme (1553) and The Pathe waye to perfectness (1569), which were among the earliest works on the subject to be published in English. Tomlin proposes that The maner and fourme is an attempt to integrate applied number work into the reformed humanist publication strategy of the King’s Printer, Richard Grafton. In The Pathe waye to perfectness Tomlin finds signs of Peele’s assertion of his authorial identity as humanist scholar. This article focuses on the title pages of Peele’s works, and considers them alongside other works printed by Grafton, to examine the ways in which these two texts position accountancy as a practice and seek to fashion the cultural capital of this particular form of number work.

[12] James Beaver’s article returns us to Robert Recorde and offers an assessment of how developments in mathematical symbolic language, and especially Recorde’s contribution to novel notational figures, including ‘=’ ‘+’ and ‘-‘, influenced John Donne’s poetics. Donne’s poetry suggests a sustained investment in quantitative language as a mode of articulation; Beaver shows that Donne’s use of the developing semiotic system of symbolic mathematics highlights the sympathies and disjunctions between this system and verbal language. He argues that quantitative language is a means of orientation for Donne, a way to organize language and perceptions, and yet, as the article explores, one that gives rise to ambiguities and anomalies. As the poet seeks to make a framework from numbers by which the abstract can be measured, number breaks down or becomes inadequate.

[13]  Stephen Deng discusses another aspect of the relationship between the new mathematics and the literary imagination, reading Shakespeare’s sonnets as an engagement with the mathematical techniques introduced to England in the sixteenth century. Deng argues that the new modes of numerical representation, and the mathematical properties that accompanied them, enabled Shakespeare to think in a varied and sustained manner through the complexity of identity, gender and sexuality. The zero, or cipher, can multiply any number by 10 simply by being added to its end, and the sonnets that seek to persuade the ‘fair youth’ to reproduce are read through this abstracted procreative power of zero. Deng shows how the cipher’s converse function, to subsume other numbers into itself through the simple operation of multiplying any number by zero, is reflected in the destructive sexuality of the ‘dark lady’ sonnets. The sonnets’ pre-occupation with the notion of identity as singular and unbroken is expressed through the newly introduced ‘broken numbers’, or fractions, and their challenge to classical notions of unity. Deng discusses these various ways in which Shakespeare used the abstracted, imaginative capacity of numbers to engage with material concerns of gender and sexuality.

[14] ‘Oh…Millions of deaths’ complains the Duke, extravagantly, as he expires in Middleton’s The Revenger’s Tragedy. Observing that quantities recur with surprising frequency in the genre of revenge tragedy, Derek Dunne draws on Middleton’s play as well as Antonio’s Revenge and Hamlet in order to quantify the reciprocal, and escalating, nature of revenge in these plays. On the one hand this can be linked to the competitive intertextuality of the genre itself, where each author tries to outdo his predecessor — the logical conclusion, perhaps, of Renaissance emulatio. But, Dunne argues, this might also point to a deeper psychology of revenge which struggles to equate life with life, and refuses to accept numerical parity.

[15] The article by Katherine Hunt considers the material qualities of numerical texts in the later seventeenth century. She investigates the numerical tables commonly found in early modern texts that were intended to be used by tradesmen, and which provided the fruits of complicated calculations at one’s fingertips. These pages full of numbers provide, Hunt argues, a material familiarity with number that was unprecedented; their structure can be compared to other varieties of printed table in the period which were used to organise and to corral knowledge. Hunt takes as her focus William Godbid and his successors, printers of mathematical and other numerical texts in late seventeenth-century London. Godbid was renowned as the best printer of high-end mathematical books, and he seems to have paid similar attention to the books he printed for merchants and tradesmen. The breadth of his output, spanning mathematical and didactic texts with profound attention to the particularities of working with number, suggests continuities — material, if not always intellectual — between texts aimed at different ends of the market, between abstract and applied number work.      

[16] The final essay completes the arc travelled by number from the mid-sixteenth to the late-seventeenth century, from exotic intellectual challenge to fashionable reading material. Katherine Ellison explores the ways of reading that cryptography manuals of the middle and late seventeenth century invited and set forth. These texts refused to confine textuality to the alphabet and promoted, Ellison argues, ciphering and deciphering as mathematic modes of reading that should be adopted in one’s everyday, and particularly domestic, life. Ellison finds these manuals to be surprisingly, and deliberately, disorderly. They are, on the one hand, concerned to portray ciphering as very learnable; on the other, they are not always concerned with conveying secret codes and secret messages, but instead often contain unsolved (or unsolvable) problems, and stress the interpretative liberty available to readers of cryptography. John Wilkins, Samuel Morland, and other authors of these books revelled in numbers: both in the quantities of ciphers that were possible, and in the use of digits to create their codes. They encouraged a familiarity with number that displays a profound understanding of Hindu-Arabic notation, of a sort which would have been barely imaginable a century earlier.

[17] Collectively, these articles point to a developing understanding of the integral place of numbers in early modern literary culture. They show how ciphers ‘filled up the number’ but also demonstrate the many ways in which number filled up the early modern page. The development of the new mathematics over the course of our period brought changes to the writing of number — from Robert Recorde’s lessons discussed in Wilde’s article, to the alphanumeric codes described in Ellison’s — which brought about profound changes to the relationships between letters and numbers in the popular imagination. We close with an afterword by Carla Mazzio which asks whether we have, in our own moment, undergone a comparable shift in our collective understanding of the relationship between numbers and writing. As literary study begins to explore the implications of our developing ability to grapple with big data, will writing be read using numbers rather than letters? There is considerable disquiet among literary scholars at such a proposition and, as Mazzio suggests, the essays collected here argue in favour of the continuing value of ‘zooming in’, of microscopic attention to written texts as well as the wide-angled possibilities of the digital humanities. Mazzio’s afterword — and her own forthcoming book, Trouble with Numbers: The Drama of Mathematics in the Age of Shakespeare (under contract with University of Chicago Press) which examines the aesthetically, dramatically, and emotionally productive dimensions of troubled forms of computation, calculation, and processes of thinking about (as well as through) mathematics in the early modern period— emphasises the complexity of writing with and of numbers, and suggests some exciting directions for the kind of work we propose in this issue. The meeting of numbers and writing continues to be a fruitful point of exchange; as the essays here show, it is at moments in which the contact between the two is marked by upheaval and flux that new modes of thinking emerge. Perhaps, then, we are entering a new stage of the relationship between numbers and writing, an analogue to Recorde’s new world of ‘arithmetycke by the penne’. The writing and the reading of number — for Recorde and his successors, but also for us — is unruly, but generative; written numbers prove excitingly disruptive when the merest cipher can ‘fill up’ and produce something from nothing.

[18] Many people have helped this special issue to come about. For their advice and support over the course of this project we would like to say thank you to Steven Connor, Vanessa Harding, Adam Smyth, and Sue Wiseman. We are very grateful to everyone who presented at the conference at Birkbeck in 2013, particularly the keynote speakers: Stephen Clucas, Natasha Glaisyer, and Emma Smith. For their help in the practicalities of planning and running the conference, our thanks go to Catherine Catrix, Sue Jones, Gillian Knight, Simon Smith, and Jackie Watson; we are extremely grateful to Lina Hakim for designing the conference poster and other materials. We would also like to recognise the generous sponsors of the conference: the Society for Renaissance Studies, ICAEW’s Charitable Trusts, the Royal Historical Society, and Birkbeck, University of London. We have found editing this special edition to be an exemplary process of scholarly dialogue, patience, and generosity and would like to thank the authors of all the articles collected here, and the anonymous peer reviewers for their incisive and constructive comments. We would especially like to thank Carla Mazzio for her characteristically perceptive afterword and for her verve, her encouragement and her insight over the course of this project. Finally, we would like to thank the editors of the Journal of the Northern Renaissance for their support and good humour throughout.

Katherine Hunt is a Career Development Fellow in English Literature at The Queen’s College, University of Oxford. Rebecca Tomlin is currently completing her doctoral thesis at Birkbeck, University of London.

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